AUTOMORPHISM COMMUTATORS

Commutators on ` ∞

The operators on `∞ which are commutators are those not of the form λI + S with λ 6= 0 and S strictly singular.

Positive Commutators

In this short and very elementary note, we will discuss the technique of proving estimates for solutions to certain partial differential equations using positive commutators, which is a widely used and powerful technique in particular in microlocal analysis. In order to keep the necessary prerequisites at the bare minimum, we won’t make any use of pseudodifferential operators and related microl...

Commutators of A∞ Structures

This note will be for the most part of an expository nature; many of the results here have appeared elsewhere. We would like however, to highlight the connection between Jim Stasheff’s early work on A∞ algebras in the 1960’s and the notion of sh Lie algebras (L∞ algebras) which is currently popular in mathematical physics; see, for example, [1] and [7]. This connection involves some work of Vic...

Multiparameter Riesz Commutators

It is shown that product BMO of S.-Y.A.Chang and R. Fefferman, defined on the space R1 ⊗ · · ·⊗Rdt , can be characterized by the multiparameter commutators of Riesz transforms. This extends a classical one-parameter result of R. Coifman, R. Rochberg, and G. Weiss [8], and at the same time extends the work of M. Lacey and S. Ferguson [12] and M. Lacey and E. Terwilleger [19], on multiparameter c...

On Subgroup Commutators